Detecting printed image copies using phase-space-encoded fragile watermark

ABSTRACT

The present invention is concerned with detection of a “fragile watermark” in a printed image to aid in a determination whether a document under examination is an original or a copy. The watermark may be applied by phase-space encoding data to be included in the watermark. The image may be examined on a block-by-block basis after scanning. Correlation of detected watermark strength with block brightness and/or with wave vectors used for encoding may be used to detect that the image is a copy.

CROSS REFERENCE TO RELATED APPLICATIONS

Reference is made to commonly assigned copending patent applications,Attorney Docket No. F-713 filed herewith entitled “Fragile Watermark forDetecting Printed Image Copies” in the names of Robert A. Cordery,Claude Zeller and Bertrand Haas; and Attorney Docket No. F-745 filedherewith entitled “Watermarking Method with Print-Scan Compensation” inthe name of Bertrand Haas.

BACKGROUND

This invention relates generally to the field of printed documentsecurity, and, more particularly, to detection of a watermark in aprinted image to determine whether the printed image is an original or acopy.

Advances in the arts of photocopying and digital image scanning andprinting have made it increasingly easy to make copies of printeddocuments with rather high fidelity such that it is difficult todistinguish between an original printed document and a photocopy orscanned-and-printed copy of the original document. These advances haveimplications in regard to such secure documents as postage meterindicia, paper currency, and event and travel tickets. Therefore, it isdesirable to provide secure documents with printed images thatincorporate special features, sometimes referred to as “fragilewatermarks”, wherein copying of the printed image results in changes ofthe feature in the copy relative to the original image in a manner thatcan be detected with a degree of reliability and convenience.

SUMMARY

Accordingly, methods are provided for examining a printed image todetermine an extent to which a fragile watermark is present in theprinted image.

In one aspect, a method is provided for determining whether aprinted-image-under-examination (PIUE) is a copy of an original printedimage. The method includes scanning the PIUE to generate scanned imagedata. The scanned image data includes pixel data, and the pixel dataincludes gray scale values and represents the PIUE as a set of scanningpixels. The method further includes forming a plurality of data blocksfrom the scanned image data. Each data block consists of pixel datawhich corresponds to a respective region of the PIUE. The method alsoincludes transforming the pixel data in at least some of the data blocksto obtain transform domain data. The method further includes applying awatermark detecting operation to the transform domain data forrespective ones of the data blocks to generate recovered watermark data.In addition, the method includes determining a correlation between therecovered watermark data for at least some of the data blocks andbrightness levels for the data blocks.

It may be determined that the PIUE is a copy of the original printedimage if the strength of the recovered watermark data is negativelycorrelated with the brightness levels for the data blocks.

The obtaining of the transform domain data may include applying at leastone of a Fourier transform, a fast Fourier transform, a discrete cosinetransform (DCT) and a wavelet transform to the pixel data.

The watermark detecting operation may include multiplying the transformdomain data with a detecting function and applying an envelope functionand then applying an inverse transform. The detecting function may bee^(ikr), where k and r are phase space indices that are applicable tothe transform domain data.

The PIUE may be part of a postal indicia, and the regions of the PIUE towhich the data blocks correspond may at least partially overlap witheach other.

In a further aspect, a method is provided for determining whether aprinted-image-under-examination (PIUE) is a copy of an original printedimage. The original printed image includes a watermark applied to theimage using a plurality of wave vectors. The method includes scanningthe PIUE to generate scanned image data. The scanned image data includespixel data, and the pixel data includes gray scale values and representsthe PIUE as a set of scanning pixels. The method further includesforming a plurality of data blocks from the scanned image data. Eachdata block consists of pixel data which corresponds to a respectiveregion of the PIUE. The method also includes transforming the pixel datain at least some of the data blocks to obtain transform domain data. Themethod further includes applying a watermark detecting operation to thetransform domain data for respective ones of the data blocks to generaterecovered watermark data. In addition, the method includes determiningat least one of (i) a correlation between the recovered watermark datafor at least some of the data blocks and brightness levels for the datablocks, and (ii) a correlation between the recovered watermark data andthe wave vectors.

In another aspect, a method of applying a watermark to an image includesproviding image data that represents the image, and providing a messagestring that includes a plurality of message bits. The method furtherincludes arraying the message bits of the message string at points of aD4 lattice, the lattice being formed as a product of a two-dimensionalposition-domain lattice and a two-dimensional frequency-domain lattice.The method also includes generating watermark image data by convolvingeach of the message bits with a respective watermark function inaccordance with a position of the respective bit in the D4 lattice. Inaddition, the method includes combining the watermark image data withthe original image data to generate combined image data.

Pixel values of the combined image data may be transformed, and an imagemay be printed using the transformed pixel values.

The arraying of the message bits may be performed such that the messagebits are arrayed only at lattice points having indices that sum to aneven number, or only at lattice points that sum to an odd number.

Each of the watermark functions may be formed by multiplying a sinusoidwith an envelope function.

A fragile watermark applied with phase-space encoding may reveal copyingof an original document since copying may degrade the strength of thewatermark in correlation with brightness levels of parts of the imageand/or in correlation with shorter wave lengths of the watermark. Bydetecting such correlation, a document examination process may be ableto conveniently and reliably identify images that are copies rather thanoriginals.

Therefore, it should now be apparent that the invention substantiallyachieves all the above aspects and advantages. Additional aspects andadvantages of the invention will be set forth in the description thatfollows, and in part will be obvious from the description, or may belearned by practice of the invention. Various features and embodimentsare further described in the following figures, description and claims.

DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate presently preferred embodiments ofthe invention, and together with the general description given above andthe detailed description given below, serve to explain the principles ofthe invention. As shown throughout the drawings, like reference numeralsdesignate like or corresponding parts.

FIG. 1 is a block diagram that illustrates an apparatus provided inaccordance with the invention for incorporating a phase-space encodedfragile watermark in an image that is part of a postage meter indicia.

FIG. 2 is a flow chart that illustrates a process that may be providedin accordance with the invention for generating and printing watermarkedimages.

FIG. 3 is a graph that illustrates a transformation that may be appliedto pixel values of an image to simulate changes in pixel values that mayresult from scanning a printed gray-scale image and then printing a copyof the image using data generated by the scanning of the printed image.

FIG. 4 is a flow chart that illustrates some details of a step of theprocess of FIG. 2.

FIG. 5 is a block diagram of an apparatus that may be provided inaccordance with the invention to examine printed images to determinewhether the printed images are originals or copies.

FIG. 6 is a flow chart that illustrates a process that may be providedin accordance with the invention to examine a printed image to determinewhether the printed image is an original or a copy.

FIG. 7 is a somewhat distorted illustration of a watermark recoveredfrom an original printed document in regard to a particular wave vectorused to encode the watermark.

DETAILED DESCRIPTION

In the method of the present invention, a watermark that is encoded inphase space is impressed on a gray scale image. The watermark is suchthat the distortions that result from scanning and reprinting fromscanned data tend to weaken the strength of the watermark in correlationwith brightness levels found in the image and in correlation with wavevectors used to encode the watermark. To determine whether a printeddocument is an original with the watermark substantially intact, or acopy in which the watermark has been compromised, the printed documentis scanned, and a block-by-block analysis of the resulting data isperformed to determine whether variations in strength in the recoveredwatermark correlate with image brightness or with the encoding wavevectors.

Referring now to the drawings, and particularly to FIG. 1, the referencenumeral 100 indicates generally an apparatus for printing watermarkedimages in accordance with principles of the present invention. Theprinting apparatus 100 includes a postage meter 102. The postage meter102, in turn, includes a printer 104 and control circuitry 106 that iscoupled to, and controls operation of, the printer 104. (Althoughembodiments of the present invention are described herein in the contextof postage metering, those who are skilled in the art will recognizethat the methods of the invention may also be applied to production andverification of other types of secure documents, including papercurrency, travel and event tickets, and identification documents.) Theprinter 104 may be of a type that is capable of printing gray scaleimages. For example, the printer 104 may include a dye-sublimationprinter. In some embodiments, the printer may be capable of printing 32or 256 gray levels.

The printing apparatus 100 also includes a data center 108 that is incommunication with the control circuitry 106 of the postage meter 102via a data communication channel 110. The data center 108 may generate awatermarked image in accordance with the invention, and may download tothe postage meter 102 image data which represents the watermarked image.Using the downloaded image data, the postage meter 102 may print thewatermarked image as a part of postage meter indicia applied tomailpieces, which are not shown. Thus the mailpieces, and particularlythe postage meter indicia thereon, may constitute original documentswhich a postal authority may wish to verify.

FIG. 2 is a flow chart that illustrates a process performed inaccordance with the invention in the printing apparatus 100 of FIG. 1.In somewhat summary form, a watermarking process according to theinvention may include preparing the image to receive the watermark,constructing the watermark using a set of wavepackets centered on pointsin a lattice, adding the watermark to the image and post-processing thewatermarked image to prepare the watermarked image for printing. Aprocessing according to the invention is now described in more detailwith reference to FIG. 2.

Initially, at step 200, an image is selected for watermarking. In someembodiments the image may be a standard image that is required to beprinted as part of every postage meter indicia by every postage meter,or by every postage meter that is part of a program for incorporating agray scale image in postage meter indicia. In other embodiments, theimage may be one of a number of standard images, any one of which may beselected by the lessor of a postage meter as the image to beincorporated in indicia to be printed by the particular postage meter.In still other embodiments, the image may be a gray scale image that ischosen by the lessor of the postage meter from among images availablefor purchase or licensing, or may be generated by the lessor of thepostage meter. In these cases, the selected image may be sent by thelessor of the postage meter to the data center for watermarking so thatthe image can be incorporated in indicia to be printed by the particularpostage meter.

In some embodiments, the image to be watermarked may be represented bypixel data that represents, with respect to each pixel of the image, agray scale level. The number of available gray scale levels may be 256,in some embodiments. In such embodiments, each pixel may be representedby one 8-bit byte of image data, and the value of each pixel may be aninteger n, with n greater than or equal to zero and less than or equalto 255. Each value of n may correspond to a different gray scale level;in some embodiments the zero value corresponds to white (no tone), thevalue 255 corresponds to black, and each value of n corresponds to atone which is darker than the tone which corresponds to n minus one.

In some cases it may be desirable to prepare the selected image beforeapplying the watermark. For example, the contrast in the image may bereduced, low pass filtering may be applied to remove image featureswhich may interfere with the watermark, and the resolution and format ofthe image may be converted to match a standard resolution and format.

A bitmap image has a limited grayscale often given as integers in arange such as 0-255 for an 8-bit depth image. The grayscale is arepresentation of the reflectance with 0 representing black or 0reflectance and 1 representing white or 100% reflectance. The image maybe filtered to remove features that interfere with the watermark. Tosimplify image processing calculations, the filtered image may beconverted to the range [0, 1]. One simple type of linear filter is toFourier transform the image, multiply each Fourier component by a factorwhich is 1 for long wavelength Fourier components and smaller forshorter wavelength components and then apply the inverse Fouriertransform to the result. This process is equivalent to convolving theimage with a blur function.

The Fourier transform and the inverse Fourier transform of an image Iare FI = ⁢ ( I ) = N ⁢ ∑ x   ⁢   ⁢ ∑ y   ⁢ ⅇ - ⅈ ⁡ ( xk x + yk y ) · I ⁡ ( x ,y ) I = - 1 ⁢ ( FI ) = N ′ ⁢ ∑ k x   ⁢   ⁢ ∑ k y   ⁢ ⅇ ⅈ ⁡ ( xk x + yk y ) ·FI ⁡ ( k x , k y )where the normalization constants N and N′ are chosen so that theinverse is correct.

Often the image pixels are on a rectangular lattice in position spacewith coordinates (x, y)=(n_(x)/dpi_(x), n_(y)/dpi_(y)), where n_(x) andn_(x) are integers. A good choice that behaves well in the continuumlimit is N equals the area per pixel 1/(dpi_(x)dpi_(y)). With thischoice and cyclic boundary conditions, if the image size is L_(x) byL_(y) then (k_(x), k_(y))=2π(m_(x)/L_(x), m_(y)/L_(y)), andN′=1/(L_(x)L_(y)), where mx and my are integers. N′ is then the volumeper wave vector times 1/(2π)². Other choices for normalization may beused.

Following step 200 is step 202. At step 202 a pixel value transformationmay be applied to the image data which corresponds to the image. Thetransformation may substantially approximate the effect on pixel valuesof first printing the image with the type of printer employed in thepostage meter, and then scanning the resulting image with a scanner ofthe type which is to be employed to verify the postage indicia. FIG. 3is a graph that illustrates an example of the transformation that may beapplied at step 202. In the graph of FIG. 3, the vertical axiscorresponds to pixel values prior to transformation, and the horizontalaxis corresponds to pixel values to which the prior values are mapped bythe transformation. Arrow 300 represents a particular pixel gray scalevalue that is to be transformed, and arrow 302 represents the gray scalevalue of the pixel after transformation. The possible pixel values to betransformed may be restricted to a range defined by a minimum gray scalelevel 304 that the printer is able to produce and a maximum gray scalelevel 306 that the printer is able to produce. The pixel value range maybe scaled to allow head room for addition of watermark data to thepixel-value-transformed image data.

Step 204 follows step 202 in FIG. 2. At step 204 a watermark is applied,in accordance with principles of the present invention, to the imageselected at step 200, as transformed at step 202.

FIG. 4 is a flow chart that illustrates some details of the watermarkingoperation represented by step 204 in FIG. 2. At 400 in FIG. 4, a messagestring is provided. The message string may represent data such aspostage meter serial number, location of mailing, etc. The bits of themessage string may be arrayed at points in a watermark lattice. Thewatermark lattice may be a subset of a 4-dimensional lattice. The D4lattice has the densest packing in 4 dimensions and so is a preferredlattice for encoding data. A convenient representation of the D4 latticeis a sublattice of the 4-dimensional hypercubic lattice with integercoordinates (j, k, m, n). The points on the hypercubic lattice withj+k+m+n even form a D4 lattice. Alternatively, a D4 lattice formed ofthe points on the hypercubic lattice with j+k+m+n odd may be used. Byusing one of such “checkerboard” lattices, the wave vectors used inadjacent cells may be different, thereby aiding in recovery of thewatermark upon scanning and analysis of the printed image.

A 4-dimensional continuous phase-space is the product of the2-dimensional image position space and the 2-dimensional wave vectorspace of the Fourier transform of the image. The coordinates of positionspace are the coordinates (x, y) of the image pixels. The coordinates ofwave vector space are the (k_(x), k_(y)) wave vector of the Fouriertransform. The coordinates of phase space are then (x, y, k_(x), k_(y)).

An injection I is defined from the watermark lattice into thephase-space. The injection defines for each point on the watermarklattice a corresponding point in the phase space and thus acorresponding position and wave vector. A preferred injection is alinear map $\begin{bmatrix}x \\y \\k_{x} \\k_{y}\end{bmatrix} = {{M\begin{bmatrix}i \\j \\m \\n\end{bmatrix}} + \begin{bmatrix}x^{0} \\y^{0} \\k_{x}^{0} \\k_{y}^{0}\end{bmatrix}}$where M is a matrix. One form for M is a diagonal matrix with diagonal(celldim, celidim, kdim, kdim) where celidim is the spacing betweencells and kdim is spacing in wave vector space of the wavepackets. Awavepacket that is very tightly localized in wave vector space is spreadout in position space and vice versa. There is a constraint from Fouriertransform theory that celidim·kdim>2π. This constraint places a limit onthe number of wave vectors that can be used for a given cell dimension.

More specifically, for each bit in the array, steps 404 and 406 may beperformed, as indicated at 402. At step 404 the data value correspondingto the bit is placed on the real-space sublattice in accordance with theindices rx, ry, then the data value is convolved with a watermarkfunction (step 406). The watermark function may be, in some embodiments,a wavepacket. In other embodiments the watermark function may be awavelet function. A wavepacket may be defined centered on each point inthe range of the injection. This wavepacket may be concentrated in alimited wave vector range and a limited position range. A simple formfor the wavepacket is Env(x, y) sin(k_(x)x+k_(y)y+φ). Preferably, Env(x,y) is concentrated in a region with dimensions similar to the basisvectors of the rectangular lattice in position space defined by theinjection. One choice for Env is a Gaussian. It is preferable to chooseEnv so that it is continuous and the sum over the two-dimensionallattice points I of Env(x−I_(x), y−I_(y)) is equal to one independent ofx and y. This is referred to as a partition of unity.

It is desirable to have the watermark fairly uniformly distributed overthe image, without high peaks due to coherent adding of differentwavepackets. The choice of φ can influence the uniformity of thewatermark and can be selected based on a modest amount ofexperimentation to produce the most uniform watermarks.

The lattice to be used in arraying the message bits may utilize valuesof k_(x), k_(y) selected so as to avoid very short wavelengths and alsoto avoid long wavelengths at which the watermark and the image mayinterfere. The spacing of the real-space indices rx, ry may be selectedto produce a cell size that is sufficiently large to allow forsuccessful filtering of the watermark features. A typical cell size(i.e. block size) may be 20 pixels by 20 pixels. It is believed that acell size of less than 10 pixels by 10 pixels may not producesatisfactory results. The blocks may overlap with each other (i.e., neednot be discrete).

After steps 404 and 406 have been performed with respect to all of thebits of the message string, step 408 follows. At step 408, theconvolution data generated at step 406 is summed over the values of ky,kx to produce watermark data that represents a watermark “image’. Then,at step 410, the watermark is multiplied by a constant so that themaximum and minimum values are within the range [−S, S] where S is aparameter substantially less than 1. Larger values of S>0.2 may resultin fairly obvious watermarks whereas smaller values less than 0.05 mayresult in watermarks that may be difficult to detect. The result is thenadded (step 412) on a pixel by pixel basis to the transformed image datathat resulted from step 202.

After step 412 is performed, the application of the watermark indicatedby step 204 in FIG. 2 is complete. Step 206 of FIG. 2 then follows. Atstep 206, the watermarked image is subjected to a pixel valuetransformation that is the inverse of the pixel value transformationthat was applied at step 202.

With the completion of step 206, the watermarked image data is now incondition for use in printing images, and may be loaded into the postagemeter 102 (FIG. 1), as indicated at step 208 in FIG. 2. For example, thewatermarked image data may be downloaded from the data center 108 to thecontrol circuitry 106 of the postage meter 102 via the datacommunication channel 110. (Transmission of the watermarked image datafrom the data center 108 to the postage meter 102 may be protected byencryption.) Alternatively, the image data may be copied onto a floppydisk or other transportable data storage medium. The storage medium maythen be mailed to the lessor of the postage meter and used to load thewatermarked image data into the postage meter.

In any event, once the watermarked image data is present in the postagemeter 102, the control circuitry 106 may control the printer 104 toprint watermarked images (step 210, FIG. 2), based on the watermarkedimage data, as part of postage meter indicia applied to mailpieces.Depending on the intensity of the watermark and the wave vectorsselected for encoding, and also depending on the image to which thewatermark is applied, the watermark may not visibly modify the printedimage, but under magnification the watermark may be discernable as anetwork of moiré patterns across the image. The watermark data can benormalized so as to center around zero so that the watermark has no neteffect on the gray scale level of the image.

In accordance with conventional practices, the postage meter indicia mayinclude other information, including, e.g., postage amount, date,mailing location, postage meter serial number (all in human-readableform), a two-dimensional barcode, etc.

FIG. 5 is a block diagram of an image examination apparatus 500 that maybe provided in accordance with the invention to examine printed images(e.g., images included in postage indicia or purported indicia) todetermine whether the printed images are originals or copies.

The image examination apparatus 500 may include a scanner 502 to scan asubstrate 504 (e.g., a mailpiece) to generate scanned image data thatrepresents a gray scale image (not separately shown) carried on thesubstrate 504. The printed gray scale image scanned by the scanner 502may be referred to as the “printed-image-under examination” or “PIUE”.

The image examination apparatus 500 further includes a processing block506 that is coupled to the scanner 502. The processing block 506 mayprocess scanned image data generated by the scanner 502, and may storescanned image data in a memory that is not separately shown and that maybe part of the processing block 506. The processing block 506 mayinclude program storage memory as well as working memory.

The image examination apparatus 500 may further include a functionalblock 508 by which a user may enter signals to control operation of theimage examination apparatus 500. The block 508 may also allow the imageexamination apparatus 500 to provide an indication of a result of theexamination of the PIUE.

FIG. 6 is a flow chart that illustrates a process that may be performedin accordance with the invention by the image examination apparatus 500of FIG. 5 to examine a PIUE to determine whether the PIUE is an originalor a copy. In somewhat summary form, a process in accordance with theinvention for detecting whether the PIUE is an original or a copy mayinclude scanning the PIUE, detecting the watermark wavepackets in thescanned PIUE, measuring the strength of the wavepackets versus thebackground intensity and versus the wavelength of the watermark andapplying a classification algorithm to determine whether the watermarkis an original or a copy.

According to a first step 600 in the process of FIG. 6, the apparatus500 scans the PIUE via the scanner 502 to generate scanned image data.The scanned image data is made up of pixel data that is constituted bygray scale values and represents the PIUE as a set of scanning pixels.

Following step 600 is step 602, at which the scanned image data isdivided into data blocks. The data blocks may correspond to thereal-space sublattice of the phase-space lattice that was used to encodethe watermark in the image data that was provided for printing by thepostage meter. In some embodiments, the data blocks may be overlapping.

Next, as indicated at 604, each of steps 606, 608 and 610 may beperformed with respect to each of the data blocks formed at step 602.

Thus, for a particular block, step 606 indicates that a transform isapplied to the pixel data of the data block to obtain transform domaindata therefrom. In some embodiments the transform is a fast Fouriertransform. Other transforms may alternatively be used, such as a Fouriertransform, a discrete cosine transform (DCT) or a wavelet transform.Next, at step 608, a watermark detecting operation is applied to thetransform domain data obtained at step 606. The detection of thewatermark includes convolving the scanned image with a detectionfunction. The detection function has the form EnvD(x, y)exp[i(k_(x)x+k_(y)y)]. Here EnvD is a similar function to Env. Theabsolute value of the correlation function shows peaks when thedetection function is centered on the watermark wavepacket. The heightsof these peaks provide a measure of the strength of each part of thewatermark.

At step 610 (which may precede or follow steps 606, 608) the brightnessof the data block in question may be determined. This may be done, forexample, by calculating an average gray scale value of the pixels in thedata block.

After the processing of steps 606, 608, 610 is completed, step 612 isperformed. At step 612 it is determined whether there is a correlationbetween the strength of the watermark and the brightness of the variousdata blocks, and/or whether there is a correlation between the strengthof the watermark data and the wave vectors that were used to encode thewatermark in the data used to print the original image. In general, tothe extent that the strength of the watermark is negatively correlatedwith the brightness of the scanned image data blocks, and/or ispositively correlated with the wavelength of the wave vectors used toencode the watermark, the likelier it is that the PIUE is a copy ratherthan an original printed image. This is because the scanning andprinting process that may be used to generate a copy tends to destroywatermark features where the image is brighter and to the extent thatthe watermark features are encoded with shorter wavelengths.

(As used herein and in the appended claims, “wave vector” refers to aset of parameters that define a wave length and an orientation intwo-dimensional space of a waveform.)

A classifying algorithm may be employed to determine whether therecovered watermark data from the scanned image data is indicative of anoriginal printed image or a copy. In some embodiments, the classifyingalgorithm may be a linear classifier. The classifier may have beentrained with a large number of known original images and known copies oforiginal images. Other types of classifiers may be used, such as a Bayesclassifier, linear regression, linear discriminant analysis, quadraticdiscriminant analysis, logistic regression, tree-based classifiers,k-nearest neighbor classifier, support vector classifier or supportvector machine.

FIG. 7 is an image that shows, in somewhat distorted form due tolimitations of reproduction technology, a portion of a watermark thatcorresponds to a single wave vector and is recovered from an originalprinted image.

It will be appreciated that a PIUE that has been printed and thenscanned for examination will generally result in a set of scanned imagedata that is distorted as compared to the original image data. It is toprevent distortion of the watermark that the “inverse transformation” ofstep 206 is applied after application of the watermark. That is, theinverse transformation of step 206 in effect “pre-reverses” thedistortion of the print-scan process, so that there is less distortionof the watermark as detected in the examination process of FIG. 6 thanwould be the case if step 206 were not included. At the same time, it isadvantageous to include step 202, so that the appearance of the printedoriginal image produced at step 210 is substantially similar to theimage represented by the image data in its condition prior to step 202.

In some embodiments, fewer than all of the pixel blocks of the imagedata, and/or less than all of the image, may be subjected to thewatermarking process. For example, certain parts of the image may beheld back from watermarking to preserve esthetic qualities of the image.It is also possible, in some embodiments, that less than all of the PIUEmay be examined for the presence of the watermark. Also, lattices otherthan the D4 lattice may be employed in arraying the message bits.

The phase-space encoded watermarking process described herein can becombined with other types of fragile watermarks, including for examplethe tonal watermark described in co-pending, commonly-assigned patentapplication entitled “Fragile Watermark For Detecting Printed ImageCopies” (Attorney docket no. F-713).

The data to be encoded with phase-space encoding in accordance with theinvention need not be meaningful, but instead can comprise random dataor constant data (e.g., all 1's).

With the fragile watermark process described above, the resultingfeatures of the printed image are likely to be affected by the processof copying an original printed image in a manner such that theexamination process of FIG. 6 can be used to reliably distinguishbetween original printed documents (e.g., postage meter indicia) inwhich the watermark features are substantially present, and copies oforiginal printed documents, with the watermark features having beensubstantially diluted or partially or largely destroyed by thescan-print process used to make the copies. Thus the present inventioncan be of substantial value in verifying the authenticity of originaldocuments. The erosion of the watermark in images that are copies ratherthan originals may be of such a nature that it can be detected using arelatively low-quality scanner.

The words “comprise,” “comprises,” “comprising,” “include,” “including,”and “includes” when used in this specification and in the followingclaims are intended to specify the presence of stated features,elements, integers, components, or steps, but they do not preclude thepresence or addition of one or more other features, elements, integers,components, steps, or groups thereof.

A number of embodiments of the present invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention. Thepresent invention may be applied, for example, to verification ofdocuments other than postage indicia. Other variations relating toimplementation of the functions described herein can also beimplemented. Accordingly, other embodiments are within the scope of thefollowing claims.

1. A method of determining whether a printed-image-under-examination(PIUE) is a copy of an original printed image, the method comprising:(a) scanning the PIUE to generate scanned image data, the scanned imagedata comprising pixel data, the pixel data comprising gray scale valuesand representing the PIUE as a set of scanning pixels; (b) forming aplurality of data blocks from the scanned image data, each data blockconsisting of pixel data which corresponds to a respective region of thePIUE; (c) transforming the pixel data in at least some of the datablocks to obtain transform domain data; (d) applying a watermarkdetecting operation to the transform domain data for respective ones ofthe data blocks to generate recovered watermark data; and (e)determining a correlation between the recovered watermark data for atleast some of the data blocks and brightness levels for said datablocks.
 2. The method according to claim 1, further comprising: (f)determining that the PIUE is a copy of the original printed image if astrength of the recovered watermark data is negatively correlated withthe brightness levels for said data blocks.
 3. The method according toclaim 1, wherein step (c) includes applying at least one of a Fouriertransform, a fast Fourier transform, a discrete cosine transform (DCT)and a wavelet transform to the pixel data in the at least some of thedata blocks to obtain the transform domain data.
 4. The method accordingto claim 1, wherein the watermark detecting operation includesmultiplying the transform domain data with a detecting function.
 5. Themethod according to claim 4, wherein the detecting function is e^(ikr),where k and r are phase space indices applicable to the transform domaindata.
 6. The method according to claim 4, wherein the detectingoperation further includes applying an envelope function to thetransform domain data that has been multiplied by the detectingfunction.
 7. The method according to claim 6, wherein the detectingoperation further includes applying an inverse transform to thetransform domain data that has been multiplied by the detecting functionand to which the envelope function has been applied.
 8. The methodaccording to claim 1, wherein the PIUE is part of a postal indicia. 9.The method according to claim 1, wherein the regions of the PIUE towhich the data blocks correspond are at least partially overlapping witheach other.
 10. A method of determining whether aprinted-image-under-examination (PIUE) is a copy of an original printedimage, the original printed image including a watermark applied to theimage using a plurality of wave vectors, the method comprising: (a)scanning the PIUE to generate scanned image data, the scanned image datacomprising pixel data, the pixel data comprising gray scale values andrepresenting the PIUE as a set of scanning pixels; (b) forming aplurality of data blocks from the scanned image data, each data blockconsisting of pixel data which corresponds to a respective region of thePIUE; (c) transforming the pixel data in at least some of the datablocks to obtain transform domain data; (d) applying a watermarkdetecting operation to the transform domain data for respective ones ofthe data blocks to generate recovered watermark data; and (e)determining at least one of (i) a correlation between the recoveredwatermark data for at least some of the data blocks and brightnesslevels for said data blocks, and (ii) a correlation between therecovered watermark data and the wave vectors.
 11. The method accordingto claim 10, further comprising: (f) determining that the PIUE is a copyof the original printed image if a strength of the recovered watermarkdata is negatively correlated with the brightness levels for said datablocks.
 12. The method according to claim 10, further comprising: (f)determining that the PIUE is a copy of the original printed image if astrength of the recovered watermark data is positively correlated withwavelengths of the wave vectors.
 13. The method according to claim 10,wherein step (c) includes applying at least one of a Fourier transform,a fast Fourier transform, a discrete cosine transform (DCT) and awavelet transform to the pixel data in the at least some of the datablocks to obtain the transform domain data.
 14. The method according toclaim 10, wherein the watermark detecting operation includes multiplyingthe transform domain data with a detecting function.
 15. The methodaccording to claim 14, wherein the detecting function is e^(ikr), wherek and r are phase space indices applicable to the transform domain data.16. The method according to claim 14, wherein the detecting operationfurther includes applying an envelope function to the transform domaindata that has been multiplied by the detecting function.
 17. The methodaccording to claim 16, wherein the detecting operation further includesapplying an inverse transform to the transform domain data that has beenmultiplied by the detecting function and to which the envelope functionhas been applied.
 18. The method according to claim 10, wherein the PIUEis part of a postal indicia.
 19. The method according to claim 10,wherein the regions of the PIUE to which the data blocks correspond areat least partially overlapping with each other.
 20. A method of applyinga watermark to an image, the method comprising; (a) providing image datathat represents the image; (b) providing a message string that includesa plurality of message bits; (c) arraying the message bits of themessage string at points of a D4 lattice, the lattice being formed as aproduct of a two-dimensional position-domain lattice and atwo-dimensional frequency-domain lattice; (d) generating watermark imagedata by convolving each of the message bits with a respective watermarkfunction in accordance with a position of the respective bit in the D4lattice; and (e) combining the watermark image data with the image dataprovided at step (a) to generate combined image data.
 21. The methodaccording to claim 20, further comprising: (f) transforming pixel valuesof the combined image data.
 22. The method according to claim 21,further comprising: (g) printing an image using the transformed pixelvalues resulting from step (f).
 23. The method according to claim 20,wherein step (c) is performed such that the message bits are arrayedonly at lattice points having indices that sum to an even number. 24.The method according to claim 20, wherein step (c) is performed suchthat the message bits are arrayed only at lattice points having indicesthat sum to an odd number.
 25. The method according to claim 20, whereineach of the watermark functions is formed by multiplying a sinusoid withan envelope function.